hydraulics and airport engineering notes

1. 21CE210- Hydraulics and
Hydraulic machinery
Unit-1
Uniform flow

2. Open channel flow Pipe flow
Liquid flow through any channel with a
free surface subjected to atmospheric
pressure
When the liquid flows under pressure
through any conduit without having free
surface.

3. Types of Flows
1. Steady and Unsteady Flow
2. Uniform and Non-uniform Flow
3. Laminar and Turbulent Flow
4. Sub-critical, Critical and Super-critical
Flow

4. 1. Steady and Unsteady Flow
Steady flow happens if the conditions (flow
rate, velocity, depth etc) do not change with time.
The flow is unsteady if the depth is changes
with time

5. 2. Uniform and Non-uniform
Flow
If for a given length of channel, the velocity of flow,
depth of flow, slope of the channel and cross section
remain constant, the flow is said to be Uniform
The flow is Non-uniform, if velocity, depth, slope and
cross section is not constant

6. 2. Non-uniform Flow
• 1. Steady and Unsteady Flow
• 2. Uniform and Non-uniform Flow
Types of Non-uniform Flow
1. Gradually Varied Flow (GVF)
If the depth of the flow in a channel changes gradually over a
length of the channel.
2. Rapidly Varied Flow (RVF)
If the depth of the flow in a channel changes abruptly over a
small length of channel

7. 3. Laminar and Turbulent
Flow
Both laminar and turbulent flow can occur in open channels
depending on the Reynolds number (Re)
Re =
ρVR/µ
Where,
ρ = density
of water =
1000 kg/m3

8. TURBULENT
LAMINAR

9. Properties of open channel
• Prismatic : Geometric dimension of the channel, such
as c/s, slope are constant throughout. Eg: Channel
with rectangular, circular, triangular c/s are prismatic.
• Non Prismatic: Geometric dimension of the channel,
such as c/s, slope are not constant throughout the
length of the channel. Eg: all natural channels such as
river, streams.

10. Velocity Distribution
Velocity is always vary across
channel because of friction along the
boundary
The maximum velocity usually found
just below the surface

11. Velocity Distribution
Velocity is always vary across
channel because of friction along the
boundary
The maximum velocity usually found
just below the surface

12. Discharge through Open Channels
1. Chezy’s C
2. Manning’s N
3. Bazin’s Formula
4. Kutter’s
Formula

13. Discharge through Open Channels
1. Chezy’s C
2. Manning’s N
3. Bazin’s Formula
4. Kutter’s Formula
Forces acting on the water between sections 1-1 & 2-2
1. Component of weight of Water = W sin i 
2. Friction Resistance = f P L V2 
where
W = density x volume
= w (AL) = wAL
Equate both Forces:
f P L V2 = wAL sin i

14. Chezy’s Formula, V  C
m
i
f
w  C  Chezy's Constant  3
P
A  m  Hydraulic Radius  2
V  w A sin i
 1 f P

15. Chezy’s Formula,
V  C
m
i
substituteEqn. 2 & 3 in Eqn.1,
V  C m.sin i
for small values of i, sin i  tan i
 i
V  C m.i

16. 1. Manning’s
N
Chezy’s formula can also be used with Manning's Roughness
Coefficient
C = (1/n) R1/6
where
R = Hydraulic Radius
n = Manning’s Roughness Coefficient

17. Most Economical Sections
1. Cost of construction should be
minimum
2. Discharge should be maximum
Types of channels based on shape:
1. Rectangular
2. Trapezoidal
3. Circular

18. Wide open channel
• Channel with large aspect ratio (breadth/depth)
is wide open channel.
• If the breadth of the channel is greater than the
flow depth by 10 times of the channel is wide
channel.

19. Specific Energy
2g
If the c hannelbottom is taken as datum ,
Es  h  v 2
whichis called as Specific Energy
2g
whe rez  Height of bottomof channelabovedatus,
T otal Energy of flow ing fluid, E  z  h  v 2

20. Specific force
• Specific force is the sum of the pressure force
and momentum force due to the flow per unit
weight of the liquid at a section.

21. Critical flow
• It is defined as the flow at which the specific
energy is minimum or the flow corresponding
to the critical depth (depth of flow at which
the specific energy is minimum).

22. Unit 2
GRADUALLY VARIED FLOW

23. Dynamic equation of GVF
1. The channel is prismatic and the flow is steady.
2. The bed slope, So, is relatively small.
3. The velocity distribution in the vertical section is uniform and the
kinetic energy correction factor is close to unity.
4. Streamlines are parallel and the pressure distribution is
hydrostatic.
5. The channel roughness is constant along its length and does not
depend on the depth of flow.

24. WATER SURFACE PROFILES CLASSIFICATION

25. Slope
Profile designation Relative
position of y
Type of flow
zone-1 zone-2 zone-3
Adverse
S0 = 0
None
A2
A3
y > yc
y <
yc
Subcritical
Supercritical
Horizontal
S0 = 0
None
H2
H3
y > yc
y <
yc
Subcritical
Supercritical
Mild
0<S0<Sc = 0
M1
M2
M3
y > yn > yc
yn > y > yc
yn > yc> y
Subcritical
Subcritical
Supercritical
Critical
S0 = Sc > 0
C1
C2
C3
y > yc = yn
y = yc = yn
yc = yn >
y
Subcritical
Uniform - Critical
Supercritical
S1 y > y > y Subcritical
Types of Flow Profiles

26. METHODS OF SOLUTIONS OF THE GRADUALLY VARIED FLOW
1. Direct Integration
2. Graphical Integration
3. Numerical Integration
i. The direct step method (distance from depth
for regular channels)
ii. The standard step method, regular
channels (distance from depth for regular
channels)
iii. The standard step method, natural
channels (distance from depth for natural
channels)

27. Control section
• A section in which a fixed relationship exists
between the discharge and the depth of flow.
• Weirs, spillways, sluice gate are some eg of
structure which give rise to control scetions.

28. Break in grade
• Simple situations of a series of combination of
two channel section with different bed slopes
are considered, such as mild to milder, steep
to steeper, milder to mild, steeper to steep,
steep to mild, mild to steep and hz to steep.